"It's a diplomatic situation for which a solution must be found... as quickly as possible," Correa told reporters shortly after declaring victory in presidential elections, saying the Australian's fate lies "in Europe's hands."
Assange, a former computer hacker and Australian citizen, founded the WikiLeaks anti-secrecy website that enraged Washington by releasing cables and war logs relating to the wars in Iraq and Afghanistan in the biggest security breach in US history.
Assange fled to Ecuador's embassy in June after losing his battle in the British courts against extradition to Sweden, where he faces questioning over allegations of rape and sexual assault.
Ecuador granted Assange asylum in August but Britain has refused to allow him safe passage.
By helping him, Ecuador "did what it had to do in the framework of its sovereignty," Correa said, urging European courts to take up the matter.
"There can't be a problem due to asylum, it's neocolonialism," he said, reiterating Quito's demands -- safe passage or questioning of Assange by a Swedish judicial official in London.
Charismatic in his supporters' eyes and authoritarian to his foes, Correa claimed victory Sunday shortly after polling stations closed in an election he had been widely expected to win.
The first official results polls gave him 56.7 percent of the vote -- and a roughly 30-point lead over his nearest rival, banker Guillermo Lasso -- with just over a third of ballots counted.